Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab
This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficien...
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| Veröffentlicht in: | Journal of computational methods in applied mathematics Jg. 20; H. 3; S. 459 - 479 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Minsk
De Gruyter
01.07.2020
Walter de Gruyter GmbH |
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| ISSN: | 1609-4840, 1609-9389 |
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| Abstract | This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.
We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes.
Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in
functions and vectorization.
This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab.
Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use.
Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education. |
|---|---|
| AbstractList | This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.
We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes.
Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in
functions and vectorization.
This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab.
Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use.
Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education. This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes.Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-infunctions and vectorization.This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab.Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use.Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education. |
| Author | Schmidt, Anja Funken, Stefan A. |
| Author_xml | – sequence: 1 givenname: Stefan A. surname: Funken fullname: Funken, Stefan A. email: stefan.funken@uni-ulm.de organization: Institut für Numerische Mathematik, Universität Ulm, Helmholtzstraße 20, 89081 Ulm, Germany – sequence: 2 givenname: Anja surname: Schmidt fullname: Schmidt, Anja email: anja.schmidt@uni-ulm.de organization: Institut für Numerische Mathematik, Universität Ulm, Helmholtzstraße 20, 89081 Ulm, Germany |
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| Snippet | This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.
We give insights into different adaptive... This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.We give insights into different adaptive... |
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| SubjectTerms | 65N30 65N50 68N15 Adaptive Mesh Refinement Adaptivity Data structures Finite Element Method Grid refinement (mathematics) Matlab Matlab Program Quadrilaterals |
| Title | Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab |
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